Question

If the length of a rectangle is `4` cm. more than its width and the perimeter of the rectangle is `28` cm., what is the area of the rectangle?

Answer 1

`"Area" = 45 " cm"^2`

Explanation:

Let the length be `L`
and the width be `W` (with all measurements in cm.)

We are told that `L=W+4`
and
that the perimeter is `28`

Since the perimeter of a rectangle is `2(L+W)`
we have
`color(white)("XXX")2(L+W)=28`

`color(white)("XXX")2(W+4+W)=28`

`color(white)("XXX")2(2W+4)=28`

`color(white)("XXX")(2W+4)=14`

`color(white)("XXX")2W=10`

`color(white)("XXX")W=5`

and since `L=W+4`
`color(white)("XXX")L=9`

Finally
`color(white)("XXX")"Area" = L xx W = 9 xx 5 =45` (sq.cm.)